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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 6864b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6864.l2 | 6864b1 | \([0, -1, 0, 88, 0]\) | \(72765788/42471\) | \(-43490304\) | \([2]\) | \(1920\) | \(0.15509\) | \(\Gamma_0(N)\)-optimal |
| 6864.l1 | 6864b2 | \([0, -1, 0, -352, 352]\) | \(2361864386/1355211\) | \(2775472128\) | \([2]\) | \(3840\) | \(0.50167\) |
Rank
sage: E.rank()
The elliptic curves in class 6864b have rank \(1\).
Complex multiplication
The elliptic curves in class 6864b do not have complex multiplication.Modular form 6864.2.a.b
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
